 
 
 
7.3.10  Dirac distribution
The Dirac δ distribution is the distributional derivative of
the Heaviside function. This means that
and, in fact,
|  | ∫ |  | δ(x) dx= | | ⎧ ⎨
 ⎩
 | | 1 | if  0 ∈ [a,b], |  | 0 | otherwise. | 
 | 
 | 
The defining property of the Dirac distribution is that
and consequently, for c∈[a,b],
The Dirac command
represents the Dirac distribution.
- 
Dirac takes one mandatory argument and one optional argument:
- 
x, a symbol or an expression.
- Optionally, n, a nonnegative integer.
 
- Dirac(x ⟨,n ⟩) returns δ(n)(x),
where δ(n) is the nth derivative of δ.
Note that x can be a real number, for which Dirac returns 0 if x≠ 0
and ∞ otherwise. However, since δ is a distribution, not a function,
computing its value at a point makes little sense.
Examples
| int(Dirac(x-1)*sin(x),x,-1,2) | 
| int(Dirac(x-1,1)*sin(x),x,-inf,inf) | 
 
 
